UNIVERSITY OF CALIFORNIA, RIVERSIDE

OF THE DISSERTATION Zeta Functions, Complex Dimensions of Fractal Strings and Multifractal Analysis of Mass Distributions

[1]  A. Besicovitch,et al.  On the Complementary Intervals of a Linear Closed Set of Zero Lebesgue Measure , 1954 .

[2]  Michel L. Lapidus,et al.  The Riemann Hypothesis and Inverse Spectral Problems for Fractal Strings , 1995 .

[3]  J. L. Véhel,et al.  Fractional Brownian motion and data traffic modeling: The other end of the spectrum , 1997 .

[4]  M. Lapidus,et al.  A Prime Orbit Theorem for Self-Similar Flows and Diophantine Approximation , 2001, math/0111067.

[5]  Jacques Lévy Véhel,et al.  Introduction to the Multifractal Analysis of Images , 1998 .

[6]  B. Mandelbrot.  Intermittent turbulence in self-similar cascades : divergence of high moments and dimension of the carrier , 2004 .

[7]  R. Mauldin,et al.  Exact Hausdorff dimension in random recursive constructions. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[8]  B. Sapoval,et al.  Vibrations of fractal drums. , 1991, Physical review letters.

[9]  R. Mauldin,et al.  Multifractal decompositions of Moran fractals , 1992 .

[10]  Michel L. Lapidus,et al.  Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann-Zeta-Function , 1997 .

[11]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[12]  Michel L. Lapidus,et al.  Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture , 1991 .

[13]  B. Mandelbrot.  Multifractals And 1/F Noise , 1999 .

[14]  S. Jaffard.  The multifractal nature of Lévy processes , 1999 .

[15]  Jacques Lévy Véhel,et al.  Multifractal Analysis of Choquet Capacities , 1998 .

[16]  R. Ellis,et al.  LARGE DEVIATIONS FOR A GENERAL-CLASS OF RANDOM VECTORS , 1984 .

[17]  R. Mauldin,et al.  Multifractal decompositions of digraph recursive fractals , 1992 .

[18]  L. Olsen,et al.  A Multifractal Formalism , 1995 .

[19]  Michel L. Lapidus,et al.  A Tube Formula for the Koch Snowflake Curve, with Applications to Complex Dimensions , 2004, math-ph/0412029.

[20]  Michel L. Lapidus,et al.  Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation , 2003, Exp. Math..

[21]  G. Michon,et al.  On the multifractal analysis of measures , 1992 .

[22]  L. Olsen,et al.  Random Geometrically Graph Directed Self-Similar Multifractals , 1994 .

[23]  Michel L. Lapidus,et al.  Spectral and Fractal Geometry: From the Weyl-Berry Conjecture for the Vibrations of Fractal Drums to the Riemann Zeta-Function , 1992 .

[24]  Stéphane Jaffard,et al.  Oscillation spaces: Properties and applications to fractal and multifractal functions , 1998 .

[25]  Michel L. Lapidus,et al.  Random fractal strings: Their zeta functions, complex dimensions and spectral asymptotics , 2005 .

[26]  Michel L. Lapidus,et al.  The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums , 1993 .

[27]  Michel L. Lapidus,et al.  Counterexamples to the modified Weyl–Berry conjecture on fractal drums , 1996, Mathematical Proceedings of the Cambridge Philosophical Society.

[28]  Y. Meyer,et al.  Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions , 1996 .